Copyright © 2009 Chunhong Wu and Linzhang Lu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be an unitary upper Hessenberg matrix whose subdiagonal elements are all positive, let be the leading principal submatrix of , and let be a modified submatrix of . It is shown that when the minimal and maximal eigenvalues of () are known, can be constructed uniquely and efficiently. Theoretic analysis, numerical algorithm, and a small example are